A201072 T(n,k)=Number of nXk 0..6 arrays with every row and column nondecreasing rightwards and downwards, and the number of instances of each value within one of each other

7, 21, 21, 35, 70, 35, 35, 35, 35, 35, 21, 77, 514, 77, 21, 7, 749, 2611, 2611, 749, 7, 1, 972, 3937, 22440, 3937, 972, 1, 7, 127, 50334, 43308, 43308, 50334, 127, 7, 21, 3034, 4448, 1127514, 2250982, 1127514, 4448, 3034, 21, 35, 7161, 381982, 175865

Offset

1,1

Comments

Table starts

..7...21......35........35.........21.............7.............1

.21...70......35........77........749...........972...........127

.35...35.....514......2611.......3937.........50334..........4448

.35...77....2611.....22440......43308.......1127514........175865

.21..749....3937.....43308....2250982......11512566.......3558888

..7..972...50334...1127514...11512566......45244488......76714325

..1..127....4448....175865....3558888......76714325....1001060834

..7.3034..381982..20393189..473983329....4070916182...13053459189

.21.7161..206357..14766300.4102010820...93433967419..126679336122

.35.2170.1377351.158314010.3773723044.1001816580924.1146503112430

Links

R. H. Hardin, Table of n, a(n) for n = 1..143

Formula

T(n,1) = binomial(7,n modulo 7). For a 0..z array, T(n,1) = binomial(z+1, n modulo (z+1)).

Example

Some solutions for n=3 k=7
..0..0..1..1..3..4..5....0..0..1..1..3..4..4....0..0..1..1..2..4..4
..0..2..2..3..4..5..6....0..2..2..3..3..5..6....0..1..3..3..4..5..5
..1..2..3..4..5..6..6....1..2..4..5..5..6..6....2..2..3..5..6..6..6

Crossrefs

Sequence in context: A266048 A233331 A158280 * A200935 A097182 A058525

Adjacent sequences: A201069 A201070 A201071 * A201073 A201074 A201075

Keyword

nonn,tabl

Author

R. H. Hardin Nov 26 2011

Status

approved